On instanton homology of corks W_n

Abstract

We consider a family of corks, denoted $W_n$, constructed by Akbulut and Yasui. Each cork gives rise to an exotic structure on a smooth 4-manifold via a twist $\tau$ on its boundary $\Sigma_n = \partial W_n$. We compute the instanton Floer homology of $\Sigma_n$ and show that the map induced on the instanton Floer homology by $\tau: \Sigma_n \rightarrow \Sigma_n$ is non-trivial.